Math Study Guide: Topic 2: Place Value, Rounding, Decimals and Scientific Notation (pages 13-17)

Question 1

In the number 4,213.056789, which digit is in the hundreds place?

Answer 1

2

Question 2

In the number 4,213.056789, which digit is in the hundredths place?

Answer 2

5

Question 3

In the number 4,213.056789, which digit is in the units (ones) place?

Answer 3

3

Question 4

In the number 4,213.056789, which digit is in the ten thousandths place?

Answer 4

7

Question 5

In the number 4,213.056789, which digit is in the tenths place?

Answer 5

0

Question 6

In the number 4,213.056789, which digit is in the tens place?

Answer 6

1

Question 7

In the number 4,213.056789, which digit is in the thousands place?

Answer 7

4

Question 8

In the number 4,213.056789, which digit is in the thousandths place?

Answer 8

6

Question 9

In the number 4,213.056789, which digit is in the millionths place?

Answer 9

9

Question 10

In the number 4,213.056789, which digit is in the hundred thousandths place?

Answer 10

8

Question 11

In the number 4,213.056789, which digit is in the ten thousandths place?

Answer 11

7

Question 12

What is “expanded notation?”

Answer 12

“Expanded notation” is another way of writing a whole number, by multiplying each digit by the proper power of 10

Example Write 4,378 in expanded notation

4 x 1,000 + 3 x 100 + 7 x 10 + 8 (or 8 x 1)

Question 13

How do you write 4,378 “expanded notation” in exponent form?

Answer 13

4 x 10³ + 3 x 10² + 7 x 10¹ + 8 (or 8 x 10⁰)

Question 14

What is any number raised to the 0^th power?

Answer 14

1

Question 15

What do you do first when you want to “round” to a certain place?

What do you do next?

And what’s the last thing you do?

Answer 15

Look at the number immediately to the right of that place

If that number is 5, 6, 7, 8, or 9, then round the place up to the next number

If that number is 0, 1, 2, 3, or 4, then round keep the place as is

All the places right of the place become zero

Question 16

When is 4,362.18225 rounded to the nearest hundred?

Answer 16

4,000

3 is in the hundreds (not hundredths!!) place. The number to the right is 6, so round up, and make the 3 a 4.

Question 17

When is 4,362.18225 rounded to the nearest hundredth?

Answer 17

4,362.18 (or 4,362.18000)

8 is in the hundredths (not hundreds!) place. The number to the right is 2, so do not round up

Question 18

What is the best way to multiply with decimals?

Answer 18

The best way to multiply with decimals is to pretend the decimal points are not there, and then add them back later

Example: 0.233 x .41 =
233 x 41 = 9,553
Then add the five decimals back to get .09553

Question 19

Divide 43.2 by .06 = ?

Answer 19

Move the decimal point in .06 to the right two spaces, which means you also have to move the decimal point in 43.2 to the right two spaces

So, you get 4,320 ÷ 6 =

720

Question 20

What does multiplying a number by 10 do to the decimal point?

Answer 20

Multiplying by 10 moves the decimal point one place to the left

Question 21

What does multiplying a number by 10³do to the decimal point?

Answer 21

Move the decimal point three places to the right

Because multiplying a number by 10³ is the same as multiplying it by 1000 or 10 x 10 x 10

Question 22

What is multiplying by a negative power of 10 the same as?

Answer 22

Multiplying by a negative power of 10 is the same as dividing by the same positive power of 10

Example: Multiplying a number by 10^-2 is the same as dividing by 10² (or dividing by 100)

Question 23

What is “scientific notation?”

Answer 23

A number is considered in “scientific notation” when it’s represented as a product of two numbers–a number between 1 and 10, and a power of 10.

• Example:* 432 in scientific notation = 4.32 x 10²
  0. 0003592 in scientific notation = 3.592 x 10⁴