Question

homework 7: scientific notation and
comparing/ordering numbers
this is a 2-page document!
directions: write each number in scientific notation.

1. 64,000
2. 0.00000049
3. 750
4. 0.000000000152
5. 82,300,000
6. 0.09
7. 52,640
8. 127.5
9. 2,320
10. the sun’s core temperature reaches close to 27,000,000 degrees fahrenheit. write this number in scientific notation.

directions: write each number in standard form.

1. ( 5.3 \times 10^4 )
2. ( 9.92 \times 10^{-6} )
3. ( 4.1 \times 10^{-2} )
4. ( 2.726 \times 10^8 )
5. ( 8.4 \times 10^{-1} )
6. ( 1.45 \times 10^3 )
7. ( 9.392 \times 10^{-4} )
8. ( 6.02 \times 10^2 )
9. ( 3.7528 \times 10^6 )
10. the maximum upload size allowed for a file is ( 1.024 \times 10^8 ) bytes. write this number in standard form.

directions: place a < or > in the circle to complete each statement.

1. ( 3.05 \times 10^6 ) ( \bigcirc ) ( 8.25 \times 10^4 )
2. ( 5.729 \times 10^2 ) ( \bigcirc ) ( 6.84 \times 10^2 )
3. ( 2.5 \times 10^{-2} ) ( \bigcirc ) ( 7 \times 10^{-3} )
4. ( 6.27 \times 10^{-7} ) ( \bigcirc ) ( 1.8 \times 10^{-6} )

© gina wilson (all things alge

Explanation:

Let's solve some of these problems step by step. We'll pick problem 10 first: writing 27,000,000 in scientific notation.

Step 1: Recall scientific notation form

Scientific notation is in the form \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.

Step 2: Move the decimal point

For 27,000,000, we move the decimal point 7 places to the left to get \( a = 2.7 \). The number of places moved is \( n = 7 \).

Step 3: Write in scientific notation

So, \( 27,000,000 = 2.7 \times 10^7 \).

Now, problem 20: writing \( 1.024 \times 10^8 \) in standard form.

Step 1: Recall standard form

Standard form is the usual decimal form. For \( a \times 10^n \), if \( n \) is positive, we move the decimal point \( n \) places to the right.

Step 2: Move the decimal point

For \( 1.024 \times 10^8 \), we move the decimal point 8 places to the right. \( 1.024 \) becomes \( 102400000 \) (adding zeros as needed).

Now, problem 21: comparing \( 3.05 \times 10^6 \) and \( 8.25 \times 10^4 \).

Step 1: Convert to the same power of 10 (optional)

We can convert \( 3.05 \times 10^6 \) to \( 305 \times 10^4 \) (since \( 10^6 = 100 \times 10^4 \), so \( 3.05 \times 100 = 305 \)).

Step 2: Compare the coefficients

Now we have \( 305 \times 10^4 \) and \( 8.25 \times 10^4 \). Since \( 305 > 8.25 \), \( 3.05 \times 10^6 > 8.25 \times 10^4 \).

Answer:

s:

1. \( \boldsymbol{2.7 \times 10^7} \)
2. \( \boldsymbol{102400000} \)
3. \( \boldsymbol{3.05 \times 10^6 > 8.25 \times 10^4} \)