Question

For each pair of numbers below, circle the number that is greater. Estimate how many times greater. $17 \cdot 10^{8}$ or $4 \cdot 10^{8}$ $2 \cdot 10^{6}$ or $7.839 \cdot 10^{6}$ $42 \cdot 10^{7}$ or $8.5 \cdot 10^{8}$

Name: Problem 2, Chapter 7: Grade 8 Mathematics: Open Up Resources, Common Core State Standards Edition
Uploaded: 2022-01-10T02:23:19-08:00
Duration: 58 s
Channel: Erika Bustos
Description: For each pair of numbers below, circle the number that is greater. Estimate how many times greater. 17 ·10^8 or 4 ·10^8 2 ·10^6 or 7.839 ·10^6 42 ·10^7 or 8.5 ·10^8

   For each pair of numbers below, circle the number that is greater. Estimate how many times greater.
$17 \cdot 10^{8}$ or $4 \cdot 10^{8}$
$2 \cdot 10^{6}$ or $7.839 \cdot 10^{6}$
$42 \cdot 10^{7}$ or $8.5 \cdot 10^{8}$

Grade 8 Mathematics: Open Up Resources, Common Core State Standards Edition

N/A 8th Edition

Chapter 7, Problem 2

Instant Answer

Solved by Expert Erika Bustos

01/10/2022

Step 1

Since the exponents are the same, we only need to compare the coefficients. Here, 17 is greater than 4. Therefore, $17 \cdot 10^{8}$ is greater than $4 \cdot 10^{8}$. To estimate how many times greater, we divide 17 by 4, which is approximately 4. Show more…

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For each pair of numbers below, circle the number that is greater. Estimate how many times greater. $17 \cdot 10^{8}$ or $4 \cdot 10^{8}$ $2 \cdot 10^{6}$ or $7.839 \cdot 10^{6}$ $42 \cdot 10^{7}$ or $8.5 \cdot 10^{8}$

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Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small to be conveniently written in decimal form. It involves expressing a number as a product of a coefficient (usually between 1 and 10) and a power of 10, which simplifies comparison and computation.

Comparing Numbers in Scientific Notation

When comparing numbers in scientific notation, the exponent of the power of 10 plays a critical role in determining magnitude. Numbers with higher exponents are greater, and if the exponents are equal, the coefficients are compared. This technique is essential for quickly identifying which number in a pair is larger.

Order of Magnitude

Order of magnitude describes the scale or size of a number, typically in powers of ten. It provides a rough measure of the magnitude and helps in estimating how many times one number exceeds another, which is particularly useful when comparing numbers in scientific notation.

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