How to Calculate Multiplication and Division of Decimals by Powers of Ten

A step-by-step guide to multiplication and division decimals by powers of ten

Whenever you want to multiply by the power of \(10\), move the decimal over to the right-hand side with the identical number of spaces as the number of zeros or as the exponent.

To multiply any whole number via \(10\), you must multiply the numbers and then put a \(0\) after the last digit in this number.

Whenever you want to divide via the power of \(10\), move its decimal toward the left-hand side of the identical number of spaces as the number of zeros or as the exponent.

To divide any multiple of \(10\) by \(10\), you must take out the last zero digit which is in one place from the number.

Multiplication and Division of Decimals by Powers of Ten – Example 1

Divide: \(7.7÷10=\)__?
Solution:
Step 1: Count the zeros in \(10\). There is \(1\) zero in \(10\).
Step 2: Move the decimal point \(1\) place to the left in \(7.7\). So, \(7.7→0.77\)
\(7.7÷10=0.77\)

Multiplication and Division of Decimals by Powers of Ten – Example 2

Multiply: \(100×0.436=\)__?
Solution:
Step 1: Count the zeros in \(100\). There are \(2\) zeros in \(100\).
Step 2: Move the decimal point \(2\) places to the right in \(0.436\). So, \(0.436→43.6\)
\(100×0.436=43.6\)

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Exercises for Multiplication and Division of Decimals by Powers of Ten

Solve.

1. \(\color{blue}{0.065 ÷ 10}\)
2. \(\color{blue}{0.243 × 1000}\)
3. \(\color{blue}{0.8954 × 100}\)
4. \(\color{blue}{0.25 ÷ 100}\)

1. \(\color{blue}{0.0065}\)
2. \(\color{blue}{243}\)
3. \(\color{blue}{89.54}\)
4. \(\color{blue}{0.0025}\)