Expanded Notation Mastery - Grade 12

Expanded Notation Mastery

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Express the number 5,872.345 in expanded notation using powers of 10.

2. Write the number represented by the expanded form: \( (3 \times 10^4) + (0 \times 10^3) + (7 \times 10^2) + (1 \times 10^1) + (9 \times 10^0) + (2 \times 10^{-1}) + (5 \times 10^{-2}) \)

3. Which of the following is the correct scientific notation for the number 0.000000456?

4. The distance from Earth to the Sun is approximately \( 1.5 \times 10^{11} \) meters. Write this distance in standard form.

5. Any number can be written as a sum of products of its digits and powers of its  .

6. For a number represented as \( d_n d_{n-1} ... d_1 d_0 . d_{-1} d_{-2} ... \), the digit \( d_k \) is multiplied by \( 10^k \). This is known as   notation.

7. Consider the number \( (2 \times 10^3) + (5 \times 10^1) + (8 \times 10^{-2}) \). What is the standard form of this number? Explain any missing terms.

8. A number is expressed as \( (A \times 10^x) + (B \times 10^y) + (C \times 10^z) \). If \( x > y > z \), what can you infer about the relative magnitudes of the terms?

9. The number \( 7.0 \times 10^0 \) is in scientific notation.

10. In expanded notation, the value of each digit is determined by its position and multiplied by the corresponding power of 10.