Question

A tiny area on a computer chip measures 2.3 x 10^-3 mm by 1.7 x 10^-4

About how many time longer is the longer dimension than the shorter dimension?

A. 1.35
B. 6
C. 7.4
D. 13.5

Answer 1

Divide the larger decimal number value by the smaller decimal number value.

When dividing scientific notation, divide the decimal numbers first:

2.3/1.7 = 1.3529

Now divide the exponents:

10^-3 / 10^-4

Using the law of exponents, when you divide two exponents together you subtract the exponent in the denominator from the exponent in the numerator:

-3 - -4 = -3 +4 = 1

Now combine it to get:

1.3529 x 10^1

Now convert to standard form by moving the decimal one place t the right:

13.529

Round to 13.5