The working rule of multiplication of a decimal by 10, 100, 1000, etc... are:

When the multiplier is 10, 100 or 1000, we move the decimal point to the right by as many places as number of zeroes after 1 in the multiplier.

**1.** To multiply a decimal by 10, move the decimal point in
the multiplicant by one place to the right.

**For examples:**

(i) 834.7 × 10

Here we multiplied the number 834.7 by 10 so we move 1 place to the right.

**Or**,

834.7 × 10

= (8347/10) × 10

= 8347/1

= 8347

(ii) 73.5 × 10 = 735

(iii) 100.9 × 10 = 1009

**2.** To multiply a decimal by 100, move the decimal point in
the multiplicant by two places to the right.

**For examples:**

(i) 98.26 × 100

Here we multiplied the number 98.26 by 100 so we move 2 places to the right.

**Or,**

98.26 × 100

= (9826/100) × 100

= 9826/1

= 9826

(ii) 6.006 × 100 = 600.6

(iii) 0.77 × 100 = 77

**3.** To multiply a decimal by 1000, move the decimal point in the
multiplicant by three places to the right.

**For examples:**

(i) 793.41 × 1000

Here we multiplied the number 793.41by 1000 so we move 3 places to the right.

**Or,**

793.41 × 1000

= (79341/100) × 1000

= 79341 × 10

= 793410

(ii) 9.15 × 1000 = 9150

(iii) 0.017 × 1000 = 17

**4.** To multiply a decimal by 10, 100, 1000, etc. move the decimal point of the multiplicant as many places to the right as there are zeroes in the multiplier.

**For examples:**

(i) 1854.347 × 10

Here we multiplied the number by 10 so we move 1 place to the right.

(ii) 72.4 × 100

Here there is only one place after the decimal and 100 has two zeros, so we put one zero at the end of the number.

(iii) 887.43 × 1000

Only 2 places are there after the decimal, but 1000 has 3 zeros, so we put one zero at the end of the number.

**Note: **Remember that in multiplication of a decimal by 10, 100, 1000, etc. the decimal will be moved to the right by as many places as the number of zeroes in the multiplier and when the number of zeros is more than the digits after the decimal number, then extra zeros must be added to the product.

**● ****Decimal.**

**Tenth Place in Decimals****Hundredths Place in Decimals****Thousandths Place in Decimals****Whole Numbers and Decimals****Decimal Place Value Chart.****Expanded form of Decimal Fractions****Like Decimal Fractions.****Unlike Decimal Fraction.****Equivalent Decimal Fractions.****Changing Unlike to Like Decimal Fractions.****Ordering Decimals****Comparison of Decimal Fractions.****Conversion of a Decimal Fraction into a Fractional Number.****Conversion of Fractions to Decimals Numbers.****Addition of Decimal Fractions.****Problems on Addition of Decimal Fractions****Subtraction of Decimal Fractions.****Problems on Subtraction of Decimal Fractions****Multiplication of a Decimal Numbers.****Multiplication of a Decimal by 10, 100, 1000****Multiplication of a Decimal by a Decimal.****Properties of Multiplication of Decimal Numbers.****Problems on Multiplication of Decimal Fractions****Division of a Decimal by a Whole Number.****Division of Decimal Fractions****Division of Decimal Fractions by Multiples.****Division of a Decimal by a Decimal.****Division of a whole number by a Decimal.****Properties of Division of Decimal Numbers****Problems on Division of Decimal Fractions****Conversion of fraction to Decimal Fraction.****Simplification in Decimals.****Word Problems on Decimal.**

**5th Grade Numbers Page**

**5th Grade Math Problems**

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