Math Problem Statement

answer

Put numbers into standard form and change standard form numbers into ordinary numbers.

Solution

Let's go through each part of the exercise.

Left Column: Convert numbers into standard form

Standard form represents a number as a multiple of a number between 1 and 10, multiplied by a power of 10. The general form is: a×10n\text{a} \times 10^{n}

For each number:

  1. 80,000 = 8×1048 \times 10^4
  2. 10,000 = 1×1041 \times 10^4
  3. 5,000,000 = 5×1065 \times 10^6
  4. 56,000 = 5.6×1045.6 \times 10^4
  5. 640,000 = 6.4×1056.4 \times 10^5
  6. 56,700 = 5.67×1045.67 \times 10^4

Right Column: Convert standard form into ordinary numbers

For each number, move the decimal point according to the power of 10:

  1. 9×103=90009 \times 10^3 = 9000
  2. 8×105=800,0008 \times 10^5 = 800,000
  3. 8.3×105=830,0008.3 \times 10^5 = 830,000
  4. 3.3×106=3,300,0003.3 \times 10^6 = 3,300,000
  5. 3.62×105=362,0003.62 \times 10^5 = 362,000
  6. 7.96×106=7,960,0007.96 \times 10^6 = 7,960,000

Let me know if you'd like more details or explanations!

Here are 5 related questions to enhance your understanding:

  1. What is 4.5×1064.5 \times 10^6 in ordinary form?
  2. How would you write 0.00042 in standard form?
  3. What is 6×1026 \times 10^2 as a regular number?
  4. If a number is 1.2×1071.2 \times 10^7, how many digits will the ordinary number have?
  5. Convert 9,200 into standard form.

Tip: When converting to standard form, remember to move the decimal point so that you have a number between 1 and 10!

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Math Problem Analysis

Mathematical Concepts

Standard Form
Powers of Ten
Scientific Notation

Formulas

Standard form: a × 10^n
Ordinary form: Shift decimal based on power of 10

Theorems

Powers of Ten
Scientific Notation

Suitable Grade Level

Grades 7-9