Multiplication and Sectionalisation with Decimals

Multiplication with Decimals

Decimals are multiplied as if they were whole numbers, and and then the decimal point is placed in the product.

0.7 0.352 = 2464 (now y'all need to place the decimal point in the product)

To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.

    0.7      1 decimal place

0.352      iii decimal places

               A total of 4 decimal places

One time yous take constitute the sum of the decimal places in each factor, you lot know how many decimal places the product will demand after its decimal signal. Starting at the far right of the number, move the decimal signal toward the left that number of decimal places.

0.2464 (4 decimal places after the decimal point)

Example

Solve: 0.ix × 0.iii

Solution

Outset multiply ignoring the decimal points

3 9 = 27

And then place the point in the product (in this instance, two decimal places)

27  =>   0.27

0.iii 0.9 = 0.27

If necessary, add zeros to the left side of the production.

Example(ii)

Solve: 0.05 0.4

Solution

Multiply as y'all would whole numbers, ignore decimal places

   0.05

  0.4

     20

Count the number of decimal places needed for the product

0.0 5   2 decimal places

0.four   ane decimal identify

20   A total of 3 decimal places

Write zeroes in front of the whole number to place the decimal point correctly

   0.05

  0.4

 0.020

Therefore 0.05 0.four = 0.02

Dividing Decimals

1.  Move the decimal betoken in the divisor to the right to make the divisor a whole number.

2.  Move the decimal signal in the dividend the same number of places to the right.

iii.  Identify the decimal point in the quotient directly over the decimal betoken in the dividend for the concluding quotient.

iv.  Split as if working with whole numbers

At times, it may be necessary to circular a quotient to a given place value.

Instance

Solve and circular to the nearest hundredth: 1.5 0.45

Since 3 < five, rounding the answer we obtain: one.5 0.45 = three.33

Decimals with Exponents

A decimal with exponents is just the decimal multiplied past itself n times, where n is the value for the exponent.

Example

Evaluate the following expressions.

i.) (0.6) 2 = 0.half-dozen 0.6 = 0.36

two.) (0.half-dozen) 3 = 0.6 0.6 0.6 = 0.36 0.vi = 0.216