Question

2/5 u6l9 practice problems
learning target: i can represent large numbers on the number line and using powers of 10.

1. show three different ways to write the number 437,000 as a multiple of a power of 10. for example, one way is writing 437,000 as $4370 * 10^{2}$.
2. show three different ways to write the number 32 million as a multiple of a power of 10.
3. refer to the number line.

a. label the tick marks on the number line.
b. plot and label the values 2,500 and $4 * 10^{3}$ on the number line.
c. which is less, 2,500 or $4 * 10^{3}$? use estimation to compare the values.

1. refer to the number line.

a. plot and label the values 3,000,000 and $7 * 10^{6}$ on the number line.
b. which is greater, 3,000,000 or $7 * 10^{6}$? estimate how many times greater.

Explanation:

Step1: Rewrite 437,000 (Way1)

$43.7 \times 10^4$

Step2: Rewrite 437,000 (Way2)

$4.37 \times 10^5$

Step3: Rewrite 437,000 (Way3)

$43700 \times 10^1$
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Step4: Rewrite 32 million (Way1)

First, 32 million = 32,000,000.
$32 \times 10^6$

Step5: Rewrite 32 million (Way2)

$3.2 \times 10^7$

Step6: Rewrite 32 million (Way3)

$320 \times 10^5$
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Step7: Calculate number line intervals (Q3a)

Number line from 0 to $10^4=10000$, with 10 intervals. Each interval: $\frac{10000}{10}=1000$. Tick marks: $0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000$

Step8: Plot values (Q3b)

$4 \times 10^3 = 4000$. Plot 2500 (midway between 2000 and 3000) and 4000 (4th tick after 0) on the line.

Step9: Compare values (Q3c)

$4 \times 10^3 = 4000$. 2500 < 4000, so 2500 is less.
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Step10: Plot values (Q4a)

$10^7=10,000,000$, 10 intervals, each = 1,000,000. $7 \times 10^6=7,000,000$. Plot 3,000,000 (3rd tick) and 7,000,000 (7th tick) on the line.

Step11: Compare and estimate (Q4b)

$7 \times 10^6=7,000,000$. $7,000,000 > 3,000,000$. Estimate: $\frac{7000000}{3000000} \approx 2.33$, so ~2 times greater.

Answer:

1. Three ways:

• $43.7 \times 10^4$
• $4.37 \times 10^5$
• $43700 \times 10^1$

1. Three ways:

• $32 \times 10^6$
• $3.2 \times 10^7$
• $320 \times 10^5$

3.
a. Tick marks (left to right): $0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000$
b. 2500 is placed midway between the 2000 and 3000 tick marks; $4 \times 10^3$ is placed at the 4000 tick mark.
c. 2,500 is less than $4 \times 10^3$
4.
a. 3,000,000 is placed at the 3rd tick mark (each tick = 1,000,000); $7 \times 10^6$ is placed at the 7th tick mark.
b. $7 \times 10^6$ is greater, approximately 2 times greater than 3,000,000