# How many times greater is 2.6 \times 10^7 than 1.3 \times 10^5?

## Question:

How many times greater is {eq}2.6 \times 10^7 {/eq} than {eq}1.3 \times 10^5 {/eq}?

## Numbers: Evaluating Ratios

The ratio of two numbers, say, {eq}x {/eq} to {eq}y {/eq}, written as {eq}r = \frac{x}{y} {/eq} represents a particular value {eq}r {/eq} which describes by how many times number {eq}x {/eq} is greater than number {eq}y {/eq}. Given two numerical expressions of {eq}x {/eq} and {eq}y {/eq}, we can evaluate the ratio {eq}r {/eq} numerically.

## Answer and Explanation:

Given two numbers:

{eq}x = 2.6\times 10^7\\ y = 1.3\times 10^5 {/eq}

The ratio of the two numbers will show us how many times the first number is greater than the second:

{eq}r = \dfrac{x}{y} = \dfrac{2.6\times 10^7}{1.3\times 10^5} = 200 {/eq}

This number {eq}r {/eq} shows that {eq}x {/eq} is {eq}\boxed{200~\rm{times}} {/eq} greater than {eq}y {/eq}.

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from CAHSEE Math Exam: Help and Review

Chapter 10 / Lesson 14