Task Sets: Use numbers expressed in scientific notation to estimate very large or very small quantities - Common Core Math - Grade 8

A

Recall / Warm-Up

1.

What is the value of $10^3$ ?

A.

100

B.

1000

C.

10000

D.

30

2.

Simplify $10^6 \div 10^2$ as a power of 10.

3.

Round 482,000,000 to one leading digit times a power of 10.

A.

$4 \times 10^8$

B.

$5 \times 10^8$

C.

$4.82 \times 10^8$

D.

$48 \times 10^7$

B

Fluency Practice

C

Varied Practice

$Flowchart simplifying six times ten to the ninth over two times ten to the fourth into three times ten to the fifth$

1.

Complete: $\dfrac{6 \times 10^9}{2 \times 10^4} = \_\_ \times 10^{\_\_}$ .

coefficient:

exponent:

2.

Which is the correct normalized scientific notation for $0.45 \times 10^8$ ?

A.

$0.45 \times 10^8$

B.

$4.5 \times 10^7$

C.

$45 \times 10^6$

D.

$4.5 \times 10^9$

3.

How many times as much is $7 \times 10^{-5}$ than $1 \times 10^{-10}$ ?

4.

Which quantity is best estimated as $9 \times 10^{11}$ ?

A.

900,000,000,000

B.

90,000,000

C.

0.0000000009

D.

9,000

D

Word Problems

1.

A city report lists the population as 7,940,000 residents.

Estimate this population as a single digit times an integer power of 10.

2.

Use these estimates: US population $\approx 3 \times 10^8$ , world population $\approx 7 \times 10^9$ .

1.

Write each estimate in standard form: US: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ World: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

US standard form:

world standard form:

2.

About how many times larger is the world population estimate than the US population estimate?

A.

about 2 times

B.

about 20 times

C.

about 4 billion more, so 4 billion times

D.

about 70 times

3.

A human hair is about $7 \times 10^{-5}$ meters wide, while a hydrogen atom is about $1 \times 10^{-10}$ meters wide.

About how many times wider is a human hair than a hydrogen atom?

E

Error Analysis

$Comparison card showing wrong added exponents result versus correct subtracted exponents result$

1.

Priya solves:
$\frac{6 \times 10^9}{2 \times 10^4}$

Priya writes:
$\frac{6}{2} \times 10^{9+4} = 3 \times 10^{13}$

What is Priya's mistake?

A.

She should add coefficients, not divide them

B.

She should subtract exponents when dividing powers of 10

C.

She should subtract the quantities instead of dividing

D.

Her work is correct

2.

Mateo converts $4.1 \times 10^{-3}$ to standard form and writes 4100.

Which feedback best explains the error?

A.

Negative exponents mean move the decimal to the left in standard form

B.

Negative exponents mean move the decimal to the right

C.

You should change the coefficient to 41

D.

You must always keep exponent positive in scientific notation

F

Challenge / Extension

$Step ladder showing rounding nine point seven times ten to the ninth into one times ten to the tenth$

1.

A value is written as $9.7 \times 10^9$ . Round it to a single digit times a power of 10 in proper scientific notation.

2.