Example 6. Write 31,407 in expanded form.

        Answers: 31407 = 31(1000) + 4(100) + 0(10) + 7(1)

Example 7. Write the numeral 43,762,123,504,931 as words.

        Answers: forty-three trillion, seven hundred and sixty-two billion, one hundred and twenty-three million,
                        five hundred and four thousand, nine hundred and thirty-one

Example 8. Express each numeral as an expansion of its base or with multibase pieces.
    (a) 134₅ (b) 321₁₀ (c) 1101₂ (d) 613₈

        Answers: (a) 134₅ = 1(5²) + 3(5¹) + 4(5⁰) = 1(25) + 3(5) + 4(1)

            (b) 321₁₀ = 3(10²) +2(10¹) + 1(10⁰) = 3(100) + 2(10) + 1 (1)

            (c) 1101₂ = 1(2³) +1(2²) + 0(2¹) + 1(2⁰) = 1(8) + 1(4) +0(2) +1

                (d) 613₈ = 6(8²) +1(8¹) + 3(8⁰)

Example 9. Write the first 20 base 3 terms

        Answers: 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210

Example 10. Convert the following to base ten:

        (a) 134₈ (b) 23032₄ (c) 110110₂

        Answers: (a) 134₈ = 1(8²) + 3(8¹) + 4(8⁰) = 1(64) + 3(8) + 4(1) = 68

            (b) 23032₄ = 2(4⁴) + 3(4³) + 0(4²) + 3(4) + 2 = 512+192+12+2 = 718

            (c) 110110₂ =1(2⁵) + 1(2⁴) + 0 + 1(2²) + 1(2) + 0 = 32+16+4+ 2 = 54

Example 11. Convert the following base ten to requested bases:

        (a) 613 = base ₈ (b) 23250 to base ₂₀

        Answers: (a) 613₁₀ = 1145₈
 

Bases	84 = 4096	83 = 512	82 = 64	81 = 8	80 = 1	Answer/Sum
8	0	1R101	1R37	4R5	5	11458
10	0	1x512 =512	1x64 =64	4x8 =32	5x1 =5	613

Answers: (a) 23250₁₀ = 2 18 2 10₂₀

Bases	204 = 160,000	203 = 8,000	202 = 400	201 = 20	200 = 1	Answer/Sum
20	0	2R7250	18R50	2R10	10	2 18 2 108
10	0	2x8000 =16000	18x400 =7200	2x20 =40	10x1 =10	23250