Arithmetic
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Real arithmetic questions asked by students, solved step by step Every question below was submitted by a real student and answered step by step.
The answer is 240. Instead of squaring both numbers, use a^2 - b^2 = (a - b)(a + b): the difference 4 times the sum 60 gives 240 in one line.
Answer: 1,618,978.05. Align the decimal points, add the hundredths (24 + 81 = 105) so one whole carries, then add the integer parts 1,197,481 + 421,496 + 1.
The club has 34 members. Pairing up exactly means the number is even, and grouping in threes with one left over means it leaves remainder 1 on division by 3.
The magic constant is 10, read straight off the full diagonal -5 + 0 + 5 + 10. Filling the rest gives 8, -2 in row 1, 6 and 3 in row 2, 4, then -3 and -4.
The answer is 175. Multiplication comes before subtraction, so evaluate 0.6 x 963 = 577.8 first - and the decimals then cancel each other exactly.
Answer: 4.7 g = 4.7 x 10^9 ng = 4,700,000,000 ng. One nanogram is 10^-9 g, so converting to the smaller unit multiplies by 10^9 rather than dividing.
4.7 mg = 4.7 x 10^-6 kg = 0.0000047 kg. Milli means 10^-3 g and a gram is 10^-3 kg, so the two prefix steps multiply into a single factor of 10^-6.
The answer is about 194.01 oz. One kilogram is 16/0.45359237 = 35.27396195 ounces, so multiplying 5.5 by that factor gives 194.006790725 ounces exactly.
The answer is 270 km/h. Divide by 1000 m per km and multiply by 3600 s per hour; the two exact factors collapse to a single multiplication by 3.6, so 75 × 3.6 = 270.
The answer is 0.46736 m/s. Multiply by 0.3048 m per foot and divide by 60 s per minute: 92 × 0.3048 / 60, with the feet and minutes cancelling as units.
The answer is about 38.77 baht per litre. Density converts mass to volume; the chain is USD/tonne to USD/kg to USD/L to baht/L, each step one multiplication.
199 divided by 15 is 13 remainder 4, or 13 and 4/15, or 13.2666... as a decimal. Long division needs only two steps because 15 does not divide 19.
The quotient is 9/10. Dividing by a fraction means multiplying by its reciprocal, so 3/5 divided by 2/3 becomes 3/5 times 3/2, which is 9/10.
The quotient is 4.96. Write 6.25 as 25/4, then dividing by 25/4 becomes multiplying by 4/25, giving 124/25 = 4.96 with no long division at all.
The quotient is 7.297. Because the divisor 6 is a whole number, divide 43782 by 6 to get 7297 and keep the decimal point in the same column, then check by multiplying back.
The answer is 3/5 = 0.6. Multiplication and division share one precedence level, so work left to right: 0.4 × 0.75 = 0.3, and then 0.3 ÷ 0.5 = 0.6.
Multiply the digits (4 x 27 = 108) and add the decimal places (4 + 6 = 10), giving 0.0000000108 = 1.08 x 10^-8.
Answer: 0.8. Order of operations puts the multiplication first: 0.4 x 0.75 = 0.3, and only then does the 0.5 get added to give 0.8, not 0.5 to give 0.5.
Answer: 62/77, about 0.80519. Clear the decimals to get 30/154, reduce to 15/77, then subtract from 1 by writing 1 as 77/77 - no rounding needed.
The answer is the fifth root of 10, about 1.58489. The decimal exponent 0.2 is the fraction 1/5, and a unit fraction exponent always denotes a plain root.
The answer is 1/100, or 0.01. A negative exponent means take the reciprocal, so 10^-2 is one over 10 squared — the result is not a negative number at all.
The value is 2. Multiplication and division come first — 15 x 2 = 30 and -204 / 3 = -68 — leaving 100 - 30 - 68, which must be worked left to right.
Work the inner bracket first: 0.7 - 3 = -2.3, so the braces give 2.7 + 2.3 = 5. Dividing by -1/5 means multiplying by -5, giving -25.
Rewrite everything as a power of 6: 216 = 6^3 and 36 = 6^2. The expression becomes 6^-6 x 6^4 = 6^-2 = 1/36.
Answer: -10. Work inside the bracket first to get 13, turn the double negative into +2, then evaluate 4 - 3 + 2 - 13 strictly from left to right to finish.
Compute each bracket first: 17.031 and 1.8585. The subtraction inside the second bracket is what makes the final answer larger than a careless 17.031 - 2 would suggest.
The answer is 4294967295. Power towers evaluate right to left, so 2^2^2 = 16 first, then 4^16 = 2^32 = 4294967296, and subtracting 1 finishes the job.
The value is 7. Simplify the bracket first, since −2 + 5 = 3, then rewrite the subtraction of a negative, − (−3), as + 3, and work left to right: 5 − 3 + 3 + 2 = 7.
The answer is −60. The factorial 5! = 120 and the division 50 ÷ 5 = 10 are both computed before the addition and subtraction run left to right.
The answer is 693/580 ≈ 1.1948. Multiplying gives 1.386, and clearing the decimals turns the division into 1386/1160, which reduces by 2 to 693/580.
(7012 - 2148) / 4 = 4864 / 4 = 1216. The bracket is evaluated before the division, and multiplying 1216 by 4 returns 4864 as a check on both steps.
The value is about 17.4263. The numerator is 8.748 and the denominator 0.502, giving the exact fraction 4374/251 before rounding.
The value is about 19.2851. Add the numerator to 8.794, subtract to get the denominator 0.456, then divide; the answer is the exact quotient 8794/456.
The value is 192. The exponent binds only to the 8, so square first to get 64 and then multiply by 3; treating it as (8 times 3)^2 would give 576 instead.
The product is about 9946.69. Keeping 500/75 and 5000/590 as exact fractions avoids the rounding drift that turns the answer into a wrong 9946.77.
The bracket gives 1/6, dividing by 1/30 multiplies by 30 to give 5, and the second factor is -1/5, so the product is -1.
The value is about 0.14256. Each constant is evaluated separately to five decimals first, so the rounding error never reaches the fourth decimal of the quotient.
(776 + 90) x 4 = 3464. The bracket is evaluated first, then multiplied by p; the distributive check 776x4 + 90x4 gives the same 3104 + 360 = 3464.
Without brackets, -2^2 means -(2^2) = -4, while (-3/4)^2 = 9/16 is positive. Dividing left to right gives -4 x 16/9 / 8 = -8/9.
The answer is −1 1/12. The 5s cancel when multiplying −5/6 by 2/5, leaving −1/3, and combining that with −3/4 over the common denominator 12 gives −13/12.
The value is 80. Division and multiplication have equal priority, so work strictly left to right: -1000/25 = -40, then -40 x -2 = 80.
The value is 77/6, or 12 and 5/6. Because c is already negative, -c becomes +12, so the expression is 12 + 5/6 and not the -12 5/6 many students write.
Answer: 61/16 = 3.8125. Multiply before adding, rewrite 5/4 as 20/16 and 5 as 80/16, then combine the numerators to get (1 - 20 + 80)/16 = 61/16 exactly.
The answer is 13. Order of operations says finish the subtraction inside the bars first, giving -13, and only then apply the absolute value, which gives 13.
The value is 7209/7 ≈ 1029.857. Multiply to get −418/35, combine with 4/5 = 28/35 to get −78/7, then subtract that from 1041 written as 7287/7.
The answer is x = 1. When the unknown sits outside the bars the problem is pure evaluation: subtract first to get -1, then take its distance from zero.
Answer: 72 + root14. Distributing gives root14 plus 6 root144; the second term is rational because 2 x 72 = 144 is a perfect square, so it collapses to 72.
The total is 600 square metres. Half of the remaining two thirds is another one third, so the last share is also one third of the whole - and it equals 200.
The roots are x = 2, 161, 13, 21, 3, 14 and 11. Simplify the powers on the right first, then undo the operations on the left one layer at a time.
The answer is 554344. The quotient is 554344.0134, so it sits barely above an integer — carrying ln 2 to ten digits is what makes the floor safe to state.
1272 is one answer; the complete list is 1272, 2172, 2712 and 7212. The digit product must be 28 = 1 x 2 x 7 x 2, since 26, 27 and 29 cannot be built from four digits.
7065 works: 7065 - 5607 = 1458. The last digit must be 5, place value turns the condition into 999a + 90(b - c) = 6453, and a = 7 with b - c = -6 solves it.
6405 is one answer, along with 6515, 6625, 6735, 6845 and 6955. The difference always equals 999(a - d) + 90(b - c), which pins a - d = 1 and b - c = 4.
The soybean plot is 1/3 of the whole garden. Half of the remaining 2/3 is 1/2 × 2/3 = 1/3 — the same fraction as the corn, which surprises most students.
The GCD is 1. The nth term is (4n - 1)/(6n - 1), so A = 203 and B = 2999; since 2999 is prime and does not divide 203, the two share no common factor.
The greatest common divisor is 2. Numerators follow 3n - 1 and denominators 5n - 2, which give X = 152 and Y = 2498, and 152 = 2^3 x 19 while 2498 = 2 x 1249.
The HCF is 3 x 5^3 x 7^4. Take every prime the two numbers share and keep the smaller exponent - no multiplying out and no prime factorisation needed.
There are exactly 512: the nine-digit 987654321 (9A = 8888888889) and 511 pandigital ten-digit numbers. The identity S(9A) = 9b forces exactly nine borrows in 10A − A.
Three 3/4-inch pieces joined end to end make 9/4 inch, and 9/4 ÷ 3/16 = 12 pieces. Why 'how many fit' is a division, and how to divide with the reciprocal.
There are 118. Count 98 multiples of 2 and 40 multiples of 5 in the range, then subtract the 20 multiples of 10 that were counted twice.
$375. Converting 25% to the decimal 0.25 and multiplying by 1,500 gives 375, which is the same as taking one quarter of the income.
A patient needs 180 micrograms of a drug supplied at 2.0 mg per 5 cc. Convert units and use dimensional analysis to find the volume in millilitres to administer.
The answer is x = 98 + 188k, y = -189 - 399k. A frequently quoted particular solution (18, -19) is wrong: it gives 3610, because 25854 mod 188 is 98, not 18.
The answer is 597795 = 15 × 39853. The rule for 5 forces the first digit to be 5, and the rule for 3 decides how large the two inner digits are allowed to be.
594495. Divisibility by 5 forces the outer digits to be 5, and divisibility by 9 forces b + c to leave remainder 4 mod 9, so b = 9 and c = 4 maximise the number.
The largest square has side 4 cm, the GCF of 64 and 36, and the sheet yields 16 x 9 = 144 squares. Why the biggest square always gives the fewest possible pieces.
The answer is 995. The difference forces 99(a - c) = 396, so the first digit exceeds the last by 4; taking a = 9, c = 5 and the largest allowed tens digit 9 gives 995.
The answer is 32/3. Multiply the whole number by the denominator (10 × 3 = 30), add the numerator to get 32, and keep the denominator 3, since 32/3 = 10.666666666666666.
Answer: 133/10. Multiply the whole number 13 by the denominator 10 to get 130, add the numerator 3, and keep 10 underneath. As a decimal that is 13.3.
The answer is 139/8. Multiply the whole number by the denominator (17 × 8 = 136), add the numerator to get 139, and keep the denominator 8, since 139/8 = 17.375.
The answer is 8/3. Multiply the whole number by the denominator (2 × 3 = 6), add the numerator to get 8, and keep the denominator 3, since 8/3 = 2.6666666666666665.
The answer is 41/2. Multiply the whole number by the denominator (20 × 2 = 40), add the numerator to get 41, and keep the denominator 2, since 41/2 = 20.5.
The answer is 14/3. Multiply the whole number by the denominator (4 × 3 = 12), add the numerator to get 14, and keep the denominator 3, since 14/3 = 4.666666666666667.
The answer is 19/3. Multiply the whole number by the denominator (6 × 3 = 18), add the numerator to get 19, and keep the denominator 3, since 19/3 = 6.333333333333333.
The answer is 79/12. Multiply the whole number by the denominator (6 × 12 = 72), add the numerator to get 79, and keep the denominator 12, since 79/12 = 6.583333333333333.
The answer is 65/7. Multiply the whole number by the denominator (9 × 7 = 63), add the numerator to get 65, and keep the denominator 7, since 65/7 = 9.285714285714286.
Answer: -764/105 = -7 29/105. Convert all three mixed numbers to improper fractions, rewrite over the LCD 105, then combine the numerators in a single subtraction.
The result is −50/7, or −7 1/7. Convert to improper fractions 38/7, 46/5 and 118/35, rewrite over 35, then combine 190 − 322 − 118 = −250.
The answer is 6 groups, each with 9 boys and 8 girls. The group count must divide both 54 and 48, so it is at most gcd(54, 48) = 6, and 6 works exactly.
Answer: 1.379448. Rewrite 0.92 as 1 - 0.08, so the product is 1.4994 minus 0.119952 - one easy multiplication and one subtraction instead of a four-digit long multiplication.
The product is exactly 238.55. Distributing gives 9.175 times 20 = 183.5 and 9.175 times 6 = 55.05, and adding those partial products returns 238.55.
The answer is 3/125 = 0.024. The repeating decimal 1.6̄ equals 5/3, and dividing by 5/3 is the same as multiplying by 3/5, which keeps every step exact.
The product is 2/9. An even number of negative factors makes the result positive; cancel 25 against 5, 26 against 13 and the remaining 5 against 45 before multiplying.
The product is -15/2. Three negative factors make the result negative; cancelling 3 with 6, 12 with 4 and 25 with 5 before multiplying keeps every number small.
Answer: 3/4. The square bracket collapses to 1/8 + 7/8 = 1, squaring keeps it 1, dividing by 7/8 gives 8/7, and 8/7 - 1/7 = 1 feeds the final steps.
The value is 4/3. The inner numerator is -39, so the second fraction is -39/15 = -13/5; adding 7/5 gives exactly 4, which the outer division by 3 turns into 4/3.
The answer is 30. Listing the multiples of 5 in range gives only 25, 30, 35, 40, and testing each against division by 7 leaves 30 as the single survivor.
(1/6) * sqrt(8.64/1.49) = 2*sqrt(894)/149 = 0.4013. Divide inside the radical first to get 5.798658, take the square root (2.40804), then divide by 6.
Converting to ninetieths gives 210/90, 36/90, 150/90 and 105/90, so the order is 7/3 > 15/9 > 21/18 > 2/5.
The value is 25. Powers first, then division and multiplication strictly left to right: 72 / 36 = 2 and 2 * 9 = 18, so the expression becomes 49 - 18 - 6.
The value is 1/169. Powers come before the subtraction on top, and the bracket must be finished before it is squared: 9 - (-4) = 13, and 13 squared is 169.
Answer: 3/4. A self-quotient gives 1, the power quotient gives back 4/3 which cancels the standalone 4/3, and what survives is 1 + 1/4 - 1/2.
Answer: 17/18. The bracket works out to 25/16 - 9/16 = 1, dividing by 9/4 gives 4/9, and 1 + 4/9 - 1/2 over the common denominator 18 comes to 17/18.
Answer: 1/4. The first bracket is exactly 1, the middle quotient is (1/2)^2 / (2/3)^2 = 9/16, the zero power is 1, and the last quotient is simply 5/16.
Answer: 1. The first bracket is (1/2)^(-1) = 2 by the quotient rule; in the second, 1 - 5/9 equals 4/9, so the division gives exactly 1 and the bracket is 1/2.
Answer: 30. Do both multiplications first, -2 x -4 = 8 and -3 x 5 = -15, then turn each subtraction of a negative into an addition: 8 + 4 + 3 + 15 = 30 exactly.
The original price is 2,000 baht a bag. The 6,400 covers 4 bags, so each sale price is 1,600, which is 80 percent of the original; divide by 0.80.
The original price is 1,000 baht a pair. Divide 4,500 by 5 for the 900 baht sale price, then divide by 0.90 - never add 10 percent back, which would give only 990.
The original price is 2,000 baht a watch. Each sold for 1,700, which is 85 percent of the original, so divide 1,700 by 0.85 to recover the pre-discount price.
The original price is 1,600 baht a shirt. Each shirt sold for 1,200, and since 1,200 is three quarters of the original, multiply by 4/3 rather than adding 25 percent.
Raising the sale price by 25% restores the original price, not 20%, because the increase is measured against the smaller discounted base of 80 rather than 100.
The increase is 10.74% (10.735% before rounding). Subtract to get the rise 1.802, divide by the original 16.786, then multiply by 100 - not by the new price.
For a fixed distance, speed is inversely proportional to time. The new speed is S/8 against the old S/10, a ratio of 10/8 = 1.25, so the increase is 25 percent.
The factorisation is 676 = 2^2 times 13^2. Dividing by 2 twice leaves 169, which is 13 squared, so 676 is itself a perfect square, namely 26 squared.
1676 = 2^2 x 419. Dividing by 2 twice leaves 419, and trial division by every prime up to sqrt(419) = 20.47 finds no factor, so 419 is itself prime.
369³ − 219³ = 39,739,950 = 1350 × 29,437. Factoring gives 150 × 264,933, and 264,933 is divisible by 9, which supplies the missing factor of 9 in 1350.
The two values are 19/88 and 8/125. Convert 0.333... to 1/3 and 2.1333... to 32/15, collapse 3^(1/2)*3^(1/2) to 3, then simplify the negative fractional exponent.
The addition form is -2 + (-9). Subtracting 9 is the same as adding its opposite, so the operation becomes a plus and the 9 picks up a negative sign.
The addition form is -20 + 6. Subtracting a number is the same as adding its opposite, so the operation sign and the sign of the second number both flip.
The answer is 4. The distance from 3.6 up to 4 is only 0.4 while the distance down to 3 is 0.6, so 4 is the nearer whole number and wins the rounding.
The turtle ends at -850 m, and its net change in position is 0 m. Signed arithmetic gives -850 + 165 - 165 = -850, so position and change are different answers.
The answer is 36 cm. "Divides evenly both ways" means the length is a common multiple, and "shortest" makes it the LCM, found from prime factorisations.
2 / sqrt(2) = sqrt(2) = 1.41421. An index-2 radical is just an ordinary square root, and multiplying top and bottom by sqrt(2) clears the denominator.
The answer is 1/3. The greatest common factor of 3 and 9 is 3, and dividing both the numerator and the denominator by it leaves a fraction that cannot reduce further.
The answer is 2777/512, or 5 and 217/512, which is exactly 5.423828125. Only one factor of 2 cancels because 2777 is odd, so the reduction stops there.
The simplified form is 3 sqrt(22), about 14.0712. Since 198 = 9 times 22 and 22 = 2 times 11 is square-free, only the factor 9 can leave the radical.
sqrt(63) = 3 sqrt(7) = 7.93725. Because 63 = 9 x 7 and 9 is a perfect square, the 3 comes out of the radical, while the square-free 7 has to stay inside.
The simplified form is 6 sqrt(2), about 8.4853. Split 72 as 36 times 2, the largest perfect-square factor, and take the root of 36 outside the radical sign.
One possible remainder is 4. The run 115 to 125 works, and its largest member 125 leaves 125 - 121 = 4 on division by 11; the only other remainder is 6.
The answers are -2, 0, 1, 10, 4 and -5. Rewriting every subtraction as adding the opposite turns all six into additions you can read straight off a number line.
The answer is 410. The condition forces the first digit to exceed the last by 4, so minimising gives a = 4, c = 0 and the smallest unused tens digit b = 1.
The answer is 710. The difference is always 99(a − c), so 693 forces a − c = 7; taking a = 7, c = 0 and the smallest valid b = 1 gives 710.
Answer: x = 10. Evaluate the right side as 64 - 25 = 39, multiply back by 7 so that 19x + 83 = 273, subtract 83 to get 19x = 190, then divide.
Answer: x = 2. Subtract exponents so the right side is 3^2 = 9, multiply back by 3 to get 25 + x = 27, then subtract 25 - no need to expand 3^14 at all.
Answer: x = 29. Treat the bracket as the unknown divisor: it must equal 3^15 / 3^13 = 3^2 = 9, so 125 - 4x = 9, giving 4x = 116 and finally x = 116/4 = 29.
Answer: x = 13. The right side is 25 - 16 = 9, so x - 7 must be 54 / 9 = 6; because the unknown is the divisor, you divide rather than multiply.
Answer: x = 81. Divide both sides by 6^8 to get 5x + 81 = 6 x 81 = 486; only the powers of 6 cancel, because 3^4 sits on both sides as a plain factor.
X = 73,082,879/12,823,200 ≈ 5.699270. The right side is 2.8663304, dividing by 3562/3600 = 0.9894444 and adding back 40.354/14.4 = 2.8023611 recovers X.
The answer is x = 7k + 6 for any integer k, giving 6, 13, 20, 27 and so on. A remainder condition has infinitely many solutions spaced exactly 7 apart.
The answer is x = 1,291,007.34, not 1,291,008.26. Factor to 1.09x = 1407198, then divide - this is how you recover a pre-tax amount from a gross total.
The 4-part share is 768 g and the 1-part share is 192 g. Add the ratio numbers to get 5 parts, divide 960 by 5 to get 192 g per part, then multiply by 4.
The answer is about 39.9461. The correct bracket runs 39.94 to 39.95, since 39.94^2 = 1595.2036 and 39.95^2 = 1596.0025 - and not 1595.0025.
The square root is 52.021391 to six decimals. Bracket between 52² = 2704 and 53² = 2809, then two Newton iterations from 52 converge to full precision.
Answer: sqrt(400) = 20, because 20 x 20 = 400. Splitting 400 as 2^4 x 5^2 pairs the prime factors, and the radical symbol always means the positive root.
-8.4 - (-2.65) = -5.75. Two minus signs in a row become a plus, then subtract the smaller absolute value from the larger and keep the negative sign.
Pad each number to four decimal places so the columns line up: 145.1700 - 76.3006 = 68.8694, then 68.8694 - 48.1640 = 20.7054.
The answer is about 0.00202843. Factor out the first term, then use S = (r^n - 1)/(r - 1); with r = 1.25 the denominator 0.25 turns division into times 4.
357, 366 and 389 all work. Adding 4 must push the units digit past 9: the carry moves the digit sum by +4 −10 +1 = −5, and only that keeps it a multiple of 5; without a carry it would just rise by 4.
699, 798 and 897 all work. Each has digit sum 24; adding 6 forces two carries that remove 18 from the sum, leaving 12, which is still a multiple of 12.
Only 299 and 398 work. Adding 2 without a carry raises the digit sum by 2, which breaks divisibility by 4, so the units digit must be 8 or 9.
369, 378 and 387 all work. Adding 3 must trigger a carry, because without one the digit sum would rise by 3 and could never stay a multiple of 6.
The number is 406. Two conditions, 2a = c + 2 and c - a = 2, form a small system whose solution a = 4, c = 6 gives 406, and 604 - 406 = 198 exactly.
The password is 5-3-2. It is the only option whose digits are all different, whose first digit exceeds the second by 2, and whose three digits add to 10.
The land costs 1,243,656,000 F and the total outlay with 125,000,000 F of buildings is 1,368,656,000 F. The key step is 1 dam² = 100 m², not 10.
The number is 43. Writing it as 10a + b turns the second condition into 10a + b = 43(a - b), which collapses to 4b = 3a and forces the digits 4 and 3.
Union collects every element once; intersection keeps only shared ones. Here A∩B = {5}, C∩D = {3,9} and D∩A = {2}, while the unions have 7, 8 and 9 elements.
The union is {5, 6, 7, 8, 9}. Collect every element that belongs to either set and list each one once; 5 and 8 appear in both but are written only a single time.
Each jar costs 24. The person with the fewest jars is 6 short of a fair one-third share, and the 144 refund covers exactly those 6 jars, so 144 / 6 = 24.
0.0000000121 = 1.21 x 10^-8 = 0.00000121 percent, roughly one chance in 82.6 million. The decimal point moves eight places right to give the mantissa 1.21.
The answer is 3 and 41/42. Since 167 is prime it shares no factor with 42, so the fraction cannot be reduced; dividing gives quotient 3 and remainder 41.
The answer is 5.73 x 10^15. Place the decimal point after the first non-zero digit, then count the 15 places it moved left; a large number keeps a positive exponent.
The answer is 99 = 3 x 3 x 11. Divide by the smallest primes in turn: 99 splits into 9 x 11, and 9 splits again into 3 x 3, which are all prime.
The answer is −4.63 × 10⁻⁸. The decimal point moves 8 places right to reach 4.63, which forces a negative exponent, while the leading minus sign is untouched.
The decimal form is -3,000,080,000. Five of the nine place shifts use the digits of 3.00008, and the remaining four are filled with padding zeros.
The decimal form is -0.0434. A negative exponent of -2 shifts the point two places left, and the minus sign in front of the 4.34 is carried through untouched.
The decimal form is -60,000,900. The point moves seven places right, and the interior zeros of 6.00009 must all be carried across before the padding zeros are added.
The decimal form is -77,100. A positive exponent of 4 shifts the point four places right, so two zeros are appended after the digits 771 to fill the places.