Question

Caleb claims that when you multiply a number by 10, you can just write a 0 at the right end of the number. Caleb gives the example 10 times 6 to prove his claim is always true. Noah does not agree with Caleb. He gives the example 0.6 times 10 to prove that Caleb's claim is not always true. Who is correct? Explain your answer.

Answer 1

Noah is correct

Explanation:

When we multiply a whole number, (without decimal notation) by 10 we can arrive at the correct answer by adding 0 to the right end of the number. However, it is not the general rule as the above method only applies to whole numbers because we have.

10 × 5 = 50

However,

10 × 5.0 ≠ 5.00

And

10 × 0.05 ≠ 0.050

The general rule is when multiplying a number by 10 it simply means shifting the decimal place one position to the left. The result of which is for whole numbers, when we shift the decimal place one place to the left, we add a zero to the right end of the number as follows;

10 × 30 = 300

Also when we multiply a decimal (fraction) by 10 we shift the place of decimal (decimal place) one decimal place to the right as follows;

10 × 0.003 = 0.03

Therefore, simply adding 0 to the right end of a number (including numbers with decimal fraction) when the number is multiplied by 10 to get the correct result is not always true.