Contents
In this publication, we will look at how a decimal fraction can be multiplied by a natural integer or other decimal fraction. We will also analyze examples to consolidate the theoretical material.
Multiplying a decimal by a natural number
Divisor – 10, 100, 1000, 10000, etc.
To multiply a decimal by a natural number 10, 100, 1000, etc., simply move the separator comma to the right by as many zeros as the number contains.
Example 1
3,67 ⋅ 10 = 36,7
Explanation: Because there is only one zero in the number 10, then we move the comma one position to the right.
Example 2
3,67 ⋅ 100 = 367
Explanation: Because there are two zeros in the number 100, then we move the comma to two positions.
Example 3
0,357 ⋅ 10 = 3,57
Explanation: In the number 10, there is one zero, therefore, the decimal separator is shifted by one position.
Example 4
0,0043 ⋅ 1000 = 4,3
Explanation: There are three zeros in the number 1000, which means we shift the separator by three positions.
Note: if the number of zeros and, accordingly, the positions of the separator transfer is greater than the digits after the decimal point, then we add the remaining zeros at the end of the result. This also works in reverse (cf. Example 7 below).
Example 5
3,67 ⋅ 1000 = 3670
Explanation: There are three zeros in the number 1000, therefore we transfer the separator to two positions and add one zero at the end of the found number.
Divisor – any number
To multiply a decimal fraction by any natural integer, we discard the comma and perform the multiplication as if we were dealing not with a fraction, but with an ordinary number. Then we count from the end of the result obtained as many digits as were in the fractional part of the original decimal fraction, and put a comma in this place.
Example 6: find the product of the numbers 5,68 and 8.
Decision:
We remove the comma in the number 5,68 and multiply it by 8:
568 ⋅ 8 = 4544
We count two digits from the end and add a comma-separator, i.e.:
5,68 ⋅ 8 = 45,44
Note: If the decimal fraction is less than 1 (that is, the integer part is 0), then by discarding the comma, we do not take into account the zero / zeros that come at the beginning when multiplying.
Example 7: multiply a number 0,089 by 7.
Decision:
We remove the comma in the number 0,089 and, discarding the zeros, multiply it by 7:
89 ⋅ 7 = 623
Here is the reverse of the situation discussed earlier in Example 5. We count 3 digits from the end, put a comma and add zero to the left of it, i.e.:
0,089 ⋅ 7 = 0,623
Product of decimals
To multiply one decimal fraction by another, we perform almost the same steps as described in the section above – remove the commas, this time in both fractions, and multiply them as ordinary numbers. Then we count from the end of the found result as many digits as there were together in the fractional parts of both factors, and write a comma.
Example 8: find how much will be 5,615 ⋅ 2,14.
Decision:
5615 ⋅ 214 = 1201610
You need to count 5 digits from the end, because in the first multiplier there were three digits after the decimal point, in the second – two (5 = 3 + 2). Those.:
5,615 ⋅ 2,14 = 12,01610 = 12,0161
Example 9: let’s calculate how much it will be 0,24 ⋅ 3,17.
Decision:
24 ⋅ 317 = 7608
We cut off 4 digits from the end with a comma and get the answer – 0,7608.