TEK: 5.3(G) Re-Teach

Division of Decimals

The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy.

TEK: 5.3(G)

The student is expected to: solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm;

Multiply or divide a decimal by multiples of 10, 100, or 1,000

Objectives

Student will be able to:

• multiply a decimal by powers of ten.

• divide a decimal by powers of ten.

• solve real-world problems that involve multiplying and dividing decimals by powers of 10.

Marci is making a bowl of punch. She wants enough punch for each person to have 2.25 glasses. How many glasses of punch does Marci need for 10 guests?

​the same as the number of zeros the number has in standard form.

To multiply by powers of 10, move the decimal point to the right the number of places indicated by the exponent.

2.25 × 10 = 22.5 Move the decimal point to the right one place.

2.25 × 100 = 225 Move the decimal point to the right two places. All the digits are to the right of the decimal point. The product is a whole number, which is written without a decimal point.

2.25 × 1,000 = 2, 250 Move the decimal point to the right three places. Since there are only two digits to the right of the decimal point, add a zero.

Use mental math.

To multiply the decimal number 2.25 by 10, move the decimal point to the right the one place.

2.25 × 10 = 22.5

Answer the question in a complete sentence.

Marci will need 22.5 glasses of punch for 10 guests.

Introduction

​What does the problem ask?

How many glasses of punch Marci needs for 10 guests.

How can the problem be solved?

To solve the problem, Marci needs to multiply 2.25 glasses by 10 guests.

Powers are numbers written using exponents. The base is the common factor. The exponent tells how many times the base is used as a factor. Powers of 10 are multiples of 10 that are written by raising the base 10 to a whole number power.

Compare the left and right columns in the chart above. Notice that the power of 10 is

​1. A rope 3.5 meters long is cut into ten equal pieces. How long is each piece?

To find the length of each piece of rope, divide the total length of the rope by 10.

To divide a decimal number by a power of 10, move the decimal point to the left the same number of places as there are zeros in the power of ten.

3.5 ÷ 10 = 0.35 Move the decimal point to the left one place.

3.5 ÷ 100 = 0.035 Add a zero and move the decimal point to the left two places.

3.5 ÷ 1000 = 0.0035 Add two zeros and move the decimal point to the left three places.

A zero is written to the left of the decimal point when the value of the number is less than one.

Use mental math and solve the problem.

Move the decimal to the left the same number of places as there are zeros in the power of ten.

3.5 ÷ 10 = 0.35

Each piece of rope is 0.35 meters long.

Examples

How can the problem be solved?

The exponent of the power of ten is 2. To multiply, move the decimal two places to the right.

4.65 × 102 = 465

Examples

​2. Multiply.

4.65 x 102

Use mental math to multiply.

Try together

Fill in the Blanks

1. Mr. Arturo buys 22.4 liters of gas each week for his car. How many liters of gas will he buy in 10 weeks? Complete the exercises.

Fill in the Blanks

2. Divide. 36 ÷ 10³

Complete the exercises.

Fill in the Blanks

3. A tree grows 0.75 centimeters a week. How many centimeters will a tree grow in 100 weeks? Complete the exercises.

Excellent!