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U7aL13 Cooldown: Multiplying, Dividing, and Estimating Scientific Notation

Estimate how many times larger
6.1 ×10^(7) is than
2.1 ×10^(-4).

610,000,000quad0,06021

U $7$ aL $13$ Cooldown: Multiplying, Dividing, and Estimating Scientific Notation $\newline$ $1$ . Estimate how many times larger $6.1 \times 10^{7}$ is than $2.1 \times 10^{-4}$ . $\newline$ $610,000,000 \quad 0,06021$

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Exponential growth and decay: word problems

Full solution

Q. U

7

aL

13

Cooldown: Multiplying, Dividing, and Estimating Scientific Notation

\newline

1

. Estimate how many times larger

6.1 \times 10^{7}

is than

2.1 \times 10^{-4}

.

\newline

610,000,000 \quad 0,06021

Compare Exponents: First, let's compare the exponents of the scientific notation to get a rough idea of how much larger one number is than the other. $\newline$ $6.1 \times 10^7$ has an exponent of $7$ , and $2.1 \times 10^{-4}$ has an exponent of $-4$ .
Estimate Difference: To estimate, we can ignore the coefficients ( $6.1$ and $2.1$ ) for a moment and just look at the $10^7$ and $10^{-4}$ . We know that $10^7$ is $10^{7 - (-4)} = 10^{11}$ times larger than $10^{-4}$ .
Round Coefficients: Now, let's bring back the coefficients. We can round them to the nearest whole number for estimation purposes. So, $6.1$ rounds to $6$ and $2.1$ rounds to $2$ .
Estimate Magnitude: We can now estimate how many times larger $6 \times 10^7$ is than $2 \times 10^{-4}$ . Since we're estimating, we can say $6$ is about $3$ times larger than $2$ .
Combine Estimates: Combining our estimates, we have $3 \times 10^{11}$ . So, $6.1 \times 10^7$ is approximately $3 \times 10^{11}$ times larger than $2.1 \times 10^{-4}$ .

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