This page includes Number Worksheets such as counting charts, representing, comparing and ordering numbers worksheets, and worksheets on expanded form, written numbers, scientific numbers, Roman numerals, factors, exponents, and binary numbers. There are literally hundreds of number worksheets meant to help students develop their understanding of numeration and number sense. In the first few sections, there are some general use printables that can be used in a variety of situations. Hundred charts, for example, can be used for counting, but they can just as easily be used for learning decimal hundredths.
Operations With Decimals and Powers of Ten: Overview In mathematics the digits 0 to 9 and place-value position are used to represent numbers. The place a digit occupies in a written number gives its value in the number.
This is a review of material learned in Grade 5, except for the inclusion of the decimal places ten thousandths, hundred thousandths, and millionths. See the place-value chart below for a visual representation of these whole-number and decimal positions.
The large whole number in the chart above—one billion, six hundred seventy-nine million, nine hundred thirty-five thousand, five hundred—is the number of quarters, placed end to end, it would take to circle Earth at its equator.
The small decimal number in the chart represents the time in seconds it takes for a computer chip to send a signal.
Many computer operations are measured in millionths of a second. You can compare whole or decimal numbers by lining them up and comparing the place-value positions.
For example, suppose two library books have the call numbers To determine which book comes first on the shelf, compare the numbers by first lining up the decimal points. Compare the digits from left to right until you find digits in the same place that are not equal.
The decimal with the smaller digit is the smaller number and so will come first on the shelf. When you round a number to a particular place-value position, you are really finding which of two numbers is closer to the original number.
You can round any decimal to any place-value position. For example, to round 0. The 3 remains unchanged if the digit to the right is 0, 1, 2, 3, or 4. The 3 rounds to 4 increases by 1 if the digit to the right is 5, 6, 7, 8, or 9. Since the digit to the right of the 3 is 4, the 3 remains unchanged.
When 10 is multiplied by itself several times, you can use an exponent to make the notation simpler.
For example, you can write 10 x 10 x 10 x 10 as The number is read "ten to the fourth power" and is equal to 10, The exponent 4 tells us how many times 10, the base, is used as a factor.
The powers of ten are displayed in the table below. For the numbers greater than 1, the exponents are positive and correspond to the number of zeros in the standard form of the number. For the numbers less than 1, the exponents are negative and tell us the number of decimal places in the standard form.
Adding and subtracting with decimals is similar to adding and subtracting with whole numbers. Numbers must be aligned according to their place value. Remember to line up the decimal points when you add or subtract decimals. You can use zeros as placeholders.
Students multiplied and divided whole numbers and decimals in Grade 5. You may need to remind them that, when they multiply decimals, the sum of the number of decimal places in the factors should equal the number of decimal places in the product.
Below are some examples involving multiplication with decimals. You can check this multiplication by using repeated addition.
If a piece of ginger root weighs 0. Sometimes when you multiply two decimals there aren't enough digits in the result to place the decimal point. In such cases you can add as many zeros as needed on the left to place the decimal point.
Since the factors have a total of six decimal places, you must write the product with six decimal places: Dividing decimals is similar to dividing whole numbers, which students learned in Grade 5. The following example illustrates how to divide a decimal by a whole number.
Kevin skates six times around the lake on a paved bike path. If he skates a total of Divide, disregarding the decimal point. Place the decimal point in the quotient directly above the decimal point in the dividend.
When you divide a decimal by another decimal, there is one more step to follow.We can write the whole number in expanded form as follows: = (1 x ) + (5 x 10) + (9 x 1).
Decimals can also be written in expanded form. Expanded form is a way to write numbers by showing the value of each digit.
May 14, · For instance, write out various numbers using a black marker for the "ones" place and a blue marker for the "tens." Thus, you would write the number 40 with a blue "4" and a black "0." Repeat this trick with a wide range of numbers to show that place value applies across the benjaminpohle.com: 87K.
The distance between Mary's house and Diana's house is meters. Which statement about the values of the digits in the distance, in meters, between their houses is true?. The value of the 5 in the tenths place is 10 times greater than the value of the 5 in the hundredths place.
The worksheets on this page will help your child learn to understand and use place value up to 10 million. There are a range of worksheets which involve different place value tasks such as expanding numbers and writing numbers in standard form.
Write Numbers in Expanded Form Worksheets with Separate Place Value Multiplier. The expanded form worksheets on this page all involve taking a number written in conventional numeric form and rewriting it in expanded form with the place value broken out.
Write the standard form for the number which, in expanded notation, is written as follows: 9, + + 2 I've got nine thousands, three hundreds, and two ones. I don't have any tens in the expanded form, so I'll need to use a zero in the tens place to keep that slot open.