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Decimals times and divided by 10, 100, 1000

Fractions, grade 6 Lesson 15 of 22Learning

Decimals times and divided by 10, 100, 1000

Times 10
10 tenths are a unit, 10 hundredths are a tenth.

When a number is multiplied by 10, every digit becomes worth 10 times more: hundredths become tenths, tenths become units, units become tens.

TensUnits.TenthsHundredths
3.25\displaystyle 3.253.25
3.25×10\displaystyle 3.25\times1032.5
The decimal point

It looks as if the decimal point moved one place to the right: 3.25×10=32.5\displaystyle {3.25\times10}={32.5}. Times 100 – two places, times 1000 – three: 3.25×100=325\displaystyle {3.25\times100}={325}, 3.25×1000=3250\displaystyle {3.25\times1000}={3250} (a zero fills the empty place).

Divided by 10

Dividing by 10 does the opposite: units become tenths, tenths become hundredths – the point moves one place to the left. 52.3÷10=5.23\displaystyle {52.3\div10}={5.23}, 52.3÷100=0.523\displaystyle {52.3\div100}={0.523}, 52.3÷1000=0.0523\displaystyle {52.3\div1000}={0.0523}.

Exercise 1
First think: will the result be bigger or smaller?

Calculate.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        d

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          e

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            f

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              Exercise 2

              Which number is missing? 3.6×□=3600.07×□=7125÷□=1.25\displaystyle {\quad 3.6\times\square}={360 \quad\quad 0.07\times\square}={7 \quad\quad 125\div\square}={1.25}

              a

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                b

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                  c

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power