Math Lesson 7
Using Very Small and Very Large Numbers

Instruction 7-4

Estimate, Round Off, and Manipulate Very Small and Very Large Numbers | Percents and Their Interpretations | Positive Integer Powers of Non-negative Integers | Decimals, Fractions, Mixed Numbers, and Positive and Negative Integers on the Number Line | Summary

DECIMALS, FRACTIONS, MIXED NUMBERS, AND POSITIVE AND NEGATIVE INTEGERS ON THE NUMBER LINE
CA GR4 NS 1.9, CA GR5 NS 1.5

Decimals

Each digit in a number has a place value. A place value is the value given to a digit by its place in a number. The following figure shows the place values of numbers to the right and left of the decimal point.

Fractions
A fraction is part of a whole or part of a group. It might be part of a pair, half of an apple, or a three of a dozen. We use three things to show a fraction.

The number on the bottom tells us how many parts there are in the whole. The number on the top tells us how many parts we are using.

Mixed Numbers
A mixed number is a number that has a whole number and a fraction. A mixed number is similar to a fraction however there is a whole number in front of the fraction. Therefore, if you have a whole candy bar and a half of a candy bar it would be written as .

Determining Decimals, Fractions, and Mixed Numbers on Number Lines

Use the number line below to figure out what the value of A, B, C, and D are:

There are a total of four lines between any two numbers. To determine the value of each line divide one by four, giving each line the value of 0.25 or one-fourth. Now you define the value of each letter:

The letter A is lying on the third line, which means A is on the three-fourths line (0.25 + 0.25 + 0.25 = 0.75 or three-fourths). The letter A is after the -1 but before the -2, making it a negative number. Since the letter is before -2, the value of A is -1.75.

The letter B is lying on the first line between 0 and -1, which means that A is on the one-fourth line. B is after the 0 but before the -1. Therefore, the value of be is -0.25.

The letter C is lying on the second line, or in the center of the two numbers, therefore the letter C is lying on the half mark. The letter is between the numbers 1 and 2, making it a positive number. The value for C is 1.5.

Each of the values for the letters can be written as a decimal, fraction, or mixed number.

Worksheet 1 Use the Number Line to Determine the Value of Each Letter

Worksheet 2 Use the Number Line to Determine the Value of Each Letter

Worksheet 3 Use the Number Line to Determine Which Number is Greater  

Worksheet 4 Use the Number Line to Determine Which Number is Greater  

Worksheet 5 Use the Number Line to Determine Which Number is Greater

Links for Students, Parents and Teachers

Now let's do Practice Exercise 7-4 (top)

Summary

Rounding Off Numbers

To round off a number, use place-value to round decimals and whole numbers.

To round to the nearest number use place-value. Look at the digit in the place to the right of where you want to round. Determine whether the digit is greater than 5 or less than 5. Round appropriately.

Estimating

Estimation is a process for determining an answer that is close to the actual total. Estimation can be used in addition, subtraction, division, and multiplication. Estimation makes use of rounded off numbers. The easiest way to find the total of an answer, use the values of the “front” digits and then adjust the estimate by grouping the remaining digits, this is also called front-end estimation.

Estimate the sum of 347 + 874

Percents, Decimals, and Fractions

You can convert a percentage to a decimal by dividing the percentage by 100. So, 75% is equal to 0.75. Or you can convert a percent to a decimal, by moving the decimal point two places to the left.

To change a percentage to a fraction by placing the percentage over 100:

To convert fractions to decimals, you divide the numerator by the denominator.

To change a decimal to a fraction, read the decimal in words and substitute numerals for words.

0.43 reads forty-three hundredths =
   

Exponents

When working with exponents there are a few vocabulary words you need to know. Base is the number that is to be raised to a given exponent. An exponent is the number that tells how many times the base is used as a factor. And, finally power is a number obtained by raising a base to an exponent.

You can use patterns to find the value of exponents?

• 6⁴ = 6 x 6 x 6 x 6
• 6³ = 6 x 6 x 6
• 6² = 6 x 6
• 6¹ = 6
• 6⁰ = 1

Any base raised to the exponent 1 equals the base. So, 6¹ = 6
Any base raised to the exponent 0 equals1. So, 6⁰ = 1

Decimals

Each digit in a number has a place value. A place value is the value given to a digit by its place in a number.

Fractions

A fraction is part of a whole or part of a group.

The number on the bottom tells us how many parts there are in the whole. The number on the top tells us how many parts we are using.

Mixed Numbers

A mixed number is a number that has a whole number and a fraction. A mixed number is similar to a fraction however there is a whole number in front of the fraction.
    

Next Page:  Problems (top)