Standard form

• What is standard form used for?


  It is a way of writing numbers, useful for very small or large numbers.
• How is standard form written?


  Standard form is written as $a \times 10^n$, where $a$ is between 1 and 10, and $n$ is any positive or negative number.
• What is an example of standard form?


  An example of standard form is $3.1 \times 10^4$.
• What does $10^0$ equal?


  $10^0 =$$1$
• What does $10^1$ equal?


  $10^1 =$$10$
• What does $10^2$ equal?


  $10^2 =$$100$
• What does $10^3$ equal?


  $10^3 =$$1000$
• What does $10^4$ equal?


  $10^4 =$$10,000$
• What does $10^5$ equal?


  $10^5 =$$100,000$
• What does $10^6$ equal?


  $10^6 =$$1,000,000$
• How do you write 50,000 in standard form?


  50,000 in standard form is $5 \times 10^4$.
• How is $50,000$ expressed in terms of powers of 10?


  $50,000 =$$5 \times 10,000 =$$5 \times 10^4$.
• How do you express 800,000 in standard form?


  800,000 in standard form is $8 \times 10^5$.
• What does $10^{-1}$ equal?


  $10^{-1} =$$0.1$
• What does $10^{-2}$ equal?


  $10^{-2} =$$0.01$
• What does $10^{-3}$ equal?


  $10^{-3} =$$0.001$
• What does $10^{-4}$ equal?


  $10^{-4} =$$0.0001$
• What does $10^{-5}$ equal?


  $10^{-5} =$$0.00001$
• What does $10^{-6}$ equal?


  $10^{-6} =$$0.000001$
• How do you convert a negative power of 10?


  When negative, you divide.
• How do you express 0.0005 in standard form?


  0.0005 in standard form is $5 \times 10^{-4}$.
• How do you convert from standard form to an ordinary number?


  To convert from standard form to an ordinary number, simply do the multiplication.
• What is $3.51 \times 10^5$ in ordinary number form?


  $3.51 \times 10^5 =$$351,000$
• What is $3.08 \times 10^{-4}$ in ordinary number form?


  $3.08 \times 10^{-4} =$$0.000308$
• What do you do if the power is positive when converting from standard form?


  If it's positive, you multiply by 10.
• What do you do if the power is negative when converting from standard form?


  If it's negative, you divide by 10.
• How do you order numbers in standard form?


  To order numbers in standard form, look at the power of 10 to determine size.
• What is the first step in ordering numbers in standard form?


  The first step is to work out the power of 10 on each number.
• How do you rearrange numbers after ordering them in standard form?


  Rearrange them back into standard form to answer.
• What is the process for adding or subtracting numbers in standard form?


  Convert numbers from standard to ordinary form, complete calculations, then convert back to standard form.
• How do you calculate $(4.5 \times 10^5) +$$(6.45 \times 10^6)$?


  Convert to ordinary numbers: $4,500 +$$6,450,000 =$$6,495,000$.
• What is the final answer for $(4.5 \times 10^5) +$$(6.45 \times 10^6)$ in standard form?


  The final answer is $6.495 \times 10^6$.
• What is the process for multiplying or dividing numbers in standard form?


  Multiply/divide the first parts of the numbers, apply index laws to the power of 10, and check numbers are between 1 and 10.
• What is the result of <latex>(3 \times 10^3) \times (3 \times 10^0)


  The result is $9 \times 10^{3}$.
• What are the steps for adding or subtracting in standard form?


  1. Convert numbers from standard to ordinary form.
  2. Complete calculations.
  3. Convert numbers back into standard form.
• What are the steps for multiplying or dividing in standard form?

  1. Multiply/divide the first parts of the numbers.
  2. Apply index laws to the power of 10.
  3. Check numbers are between 1 and 10.
• How do you order numbers in standard form?


  1. Look at the power of 10 to determine size.
  2. If two or more numbers have the same power of 10, use the first part to determine size.
• What is the significance of the first part of a number in standard form?


  • It helps determine the size when powers of 10 are the same.
  • It must be between 1 and 10 for standard form.
• What is the difference between positive and negative powers of 10?


  • Positive powers indicate multiplication by 10.
  • Negative powers indicate division by 10.