Standard Form Home Learning (Print).pdf

Writing and Interpreting Numbers in Standard Form We use standard form to easily write very, very large numbers and very, very small numbers. A number is in standard form when it is written in the form: a × 10n a is a number greater than, or equal to 1, and less than 10. n is an integer (whole numb...

Writing and Interpreting Numbers in Standard Form We use standard form to easily write very, very large numbers and very, very small numbers. A number is in standard form when it is written in the form: a × 10n a is a number greater than, or equal to 1, and less than 10. n is an integer (whole number). If n is positive, we are dealing with a large number. If n is negative, we have a small number (less than 1). The power of n tells us how many times we multiply by 10 (if n is positive) or divide by 10 (if n is negative). Informally, we can say that n tells us how many places the digits have moved in relation to the decimal point. Example 1 Example 2 a. Write 39 000 in standard form. a. Write 3.2 × 102 as an ordinary number. We need to begin by choosing our value for This is 3.2 × 10 × 10. The value for n is positive a. We want to keep the same digits in the so we know the number is going to be a large answer so we choose 3.9. one. Since n = 2, we move the digits 2 places. 3.2 × 102 = 320 39 000 can be written as 3.9 × 10 × 10 × 10 × 10 or 3.9 × 104. b. Write 1.8 × 10-3 as an ordinary number. Look at where the decimal point would be in The value for n is negative so we know the the original number and where the decimal number is going to be a small one. point is in our new number. We can count the difference in the number of As n = -3, we could divide 1.8 by 10 three places to find the value of n. times. 39 000 Alternatively, we can move the digits 3 places. 4 places 1.8 × 10-3 = 0.0018 b. Write 0.0000467 in standard form. We begin by choosing our value for a. We want to keep the same digits in the answer so we choose 4.67 This time, we have a small number (it’s less than 1) so we are going to have a negative value of n. We can count the number of places the digits have moved. 0.0000467 5 places The digits have moved 5 places, therefore: 0.0000467 = 4.67 × 10-5 1 of 2  Writing and Interpreting Numbers in Standard Form Your Turn 1. Identify whether each of the following numbers is written in standard form. If a number is not written in standard form, explain why. a. 2 × 100.5  b. 10 × 104  c. 3 × 10-15  d. 0.9 × 10-2  e. 4.721431709 × 10-3  2. Write each number in standard form: a. 7000 d. 38 000 g. 0.00981    b. 900 000 e. 0.002 h. 0.07024    c. 120 f. 0.000045 i. 98    3. Write each number in ordinary form: a. 4 × 103 d. 9.01 × 104 g. 1.41 × 10-7    b. 2 × 107 e. 7 × 10-2   c. 3.1 × 102 f. 2.9 × 10-4   Challenge: These numbers are not in standard form. Convert each one to standard form. a. 31 × 104 b. 0.9 × 10-3   2 of 2