Multiplying and Dividing in 10s

Multiplying by 10, 100, 1000, moves the digits in each column (units, 10s, 100s, etc) to the left:

• multiplying by 10 moves all the digits 1 column to the left;

• multiplying by 100 moves the digits 2 columns to the left;

• multiplying by 1000 moves the digits 3 columns to the left.

10 000	1 000	100	10	1
			2	6
		2	6	0	x10
	2	6	0	0	x100
2	6	0	0	0	x1000

Dividing by 10, 100, 1000 moves the digits in each column to the right:

• dividing by 10 moves them 1 digit to the right;

• dividing by 100 is 2 digits right;

• dividing by 1000 is 3 digits right.

10 000	1 000	100	10	1
4	9	0	0	0
	4	9	0	0	÷10
		4	9	0	÷100
			4	9	÷1000

The same is true for decimal numbers. The digits move and the decimal point stays in the same place.

1000	100	10	1		`frac(1)(10)`	`frac(1)(100)`	`frac(1)(1000)`
			3	.	0	1	2
		3	0	.	1	2	0	x10
	3	0	1	.	2			x100
3	0	1	2	.	0			x1000

100	10	1		`frac(1)(10)`	`frac(1)(100)`
4	9	0	.	0
	4	9	.	0		÷10
		4	.	9		÷100
		0	.	4	9	÷1000

Example 1

What is 34 x 100?

Move the 34 two digits to the left, filling the empty spaces with zeroes.

Answer: 3400

Given 34 x 23 = 782, what is 34 x 230?

230 = 23 x 10, re-write the question as 34 x 23 x 10.

That makes the answer 10 times larger than the original question.

Answer: 7820