Ch 3: Decimals Flashcards
Writing And Rounding Decimals: Place Value
A decimal is a number that contains a decimal point. The decimal point separates the whole number from the part of the number less than a whole. The places to the right of the decimal point are called decimal places, and the digits in those places form the decimal part of the number. 100 Hundreds 10 Tens 1 Ones . Decimal Point .1 = 1/10 Tenths .10 = 1/100 Hundredths .100 = 1/1000 Thousandths
The whole number part and the decimal part of a number are separated by and in the word form of a number. Do not use and anywhere else when reading or writing a number.
Equivalent Decimals
Decimals that represent the same part of a whole are equivalent decimals. Placing additional zeros to the right of the last digit of the last digit of a decimal does not change the value of the decimal.
Comparing Decimals
To compare two decimals, write them so that they each have the same number of decimal places. For example, to compare 0.05 and 0.505, write 0.05 with three decimal places. When both numbers are written with the same number of decimal places, it is easier to see which is less and which is greater.
- 05 = 0.050 = fifty thousandths
- 505 = 0.505 = five hundred five thousandths
Rounding Decimals
The rules for rounding a number to a decimal place are similar to the rules for rounding a whole number. Steps 1 and 2 are the same, but Step 3 is different. Instead of inserting placeholders, you will be eliminating some digits to the right of the decimal point.
Rules for Rounding to a Decimal Place
Step 1: Identify the digit in the place you want to round to
Step 2: Look at the digit to the right. If it is 5 or greater, increase the digit in the place being rounded by one (round up). Otherwise, keep that digit the same (round down).
Step 3: Eliminate all digits to the right of the decimal place to which the number was rounded.
Adding Decimals
The key to adding whole numbers is to align the numbers so that ones are added to ones, tens are added to tens, and so on. The same is true for adding decimals. We want to add tenths to tenths, and hundredths to hundredths. If all the decimal points are written in a vertical column, this will happen automatically.
When numbers to be added do not have the same number of decimal places, write equivalent decimals so that all the numbers have he same number of decimal places.
Step 1: Write the numbers with the decimal points in a column.
Step 2: Write zeros as needed so that all the numbers have the same number of decimal places.
Step 3: Add. Write the decimal point in the sum directly below the other decimal points.
The zeros that are written to make equivalent decimals are sometimes called placeholders.
Subtracting Decimals
The key to subtracting decimals is to align the numbers so that the decimal points are written in a vertical column. Just as in addition, zeros are written as needed so that both numbers have the same number of decimal places.
When regrouping is necessary in a decimal subtraction problem, it is done the same way that it is done with whole numbers.
Step 1: Write the numbers with the decimal points in a column.
Step 2: Write zeros as needed so that both numbers have the same number of decimal places.
Step 3: Subtract. Write the decimal point in the difference directly below the other decimal points.
Multiplying Decimals
Multiplying decimals is similar to multiplying whole numbers. The difference is in the placement of the decimal point in the product. To multiply decimals, follow these steps…
Step 1: Multiply as you would multiply whole numbers.
Step 2: Find the sum of the decimal places in the factors.
Step 3: Insert a decimal point so that the number of decimal places in the product is the sum you found in Step 2. If the decimal is less than 1, it is preferred to write a zero in the ones place.
When a product represents dollars and cents, round it to the nearest hundredth.
Dividing Decimals
When the divisor in a division problem is a whole number and the dividend is a decimal, place the decimal point in the quotient directly above the decimal point in the dividend. Then divide as you would with whole numbers.
When the divisor contains one or more decimal places, follow these steps…
Step 1: Move the decimal point in the divisor to the right until the divisor becomes a whole number.
Step 2: Move the decimal point in the dividend to the right the same number of places you moved the decimal point in the divisor. Place the decimal point in the quotient directly above the newly established decimal point in the dividend.
Step 3: Divide.
In division of decimals, the placement of the decimal point is done before dividing. This is unlike multiplication of decimals, where the placement of the decimal point is done after multiplying.
Converting Decimals And Fractions: Decimal to a Fraction or a Mixed Number
A A decimal number less than 1 can be converted to a proper fraction To convert, use the word form of the decimal number. The first part of the word form is the numerator of the fraction, and the second part is the denominator. The decimal 0.03 is converted below…
0.03 = three hundredths = 3/100
A decimal number greater than 1 can be converted to a mixed number part remains the same, and the decimal part is converted to a fraction.
Fraction or Mixed Number to a Decimal
Using division, any proper fraction can be converted to a decimal. Divide the numerator by the denominator to convert a fraction to a decimal.. In some cases, the division will result in a remainder of zero. In other cases, no matter how many zeros are annexed, there will always be a remainder.
The symbol ~ means “is approximately equal to.”
Reading A Metric Rule
Many lengths in the metric system of measurement are given in millimeters (mm), centimeters (cm), and meters (m). One meter is equal to 100 centimeters, or 1000 millimeters. One centimeter is equal to 10 millimeters.
Every centimeter on this ruler is divided into 10 equal parts by tick marks. The distance between each pair of tick marks is 1/10 centimeter, or 1 millimeters.
