11 Counting and Numerals Homework
For each two sets noted, indicate whether or not the sets match. If they do, show a matching. If they do not, explain why not.
a. Small Blue A-blocks and Large Red A-Blocks
b. Yellow A-blocks and Circular A-blocks
Describe a matching between the set of counting numbers, {1, 2, 3, …} and the set of positive multiples of five, {5, 10, 15, …}.
Show every possible one-to-one correspondence between the Small Blue A-blocks and the Small Red A-blocks. Use abbreviations or pictures to denote the blocks.
Convert each numeral to a Hindu-Arabic Base Ten numeral.
| a. STROKE: | | | | | | | | | | | | | | | | |
| b. Tally: [latex]\cancel{||||}\cancel{||||}\cancel{||||} |||[/latex] |
| c. Roman: MCMLXII |
| d. Roman: DCCXLIV |
| e. Roman: [latex]\bar{\bar{\text{IV}}\text{CCX}}[/latex]DLI |
|
f. Egyptian: π¨ π π π¨ πΌ β© β© π¨ π |
|
g. Chinese ε ε ε ε δΈ |
|
h. Mayan π§ π π° π£ |
| i. [latex]4032_{\text{seven}}[/latex] |
| j. [latex]T6W_{\text{thirteen}}[/latex] |
| k. [latex]1 111 001 011_{\text{two}}[/latex] |
| l. [latex]507_{\text{nine}}[/latex] |
Convert 342 to a numeral in the numeration system or base specified.
| a. Roman | b. Base Seven | c. Egyptian |
| d. Base Two | e. Chinese |
Convert 838 to:
| a. Base Twelve | b. Base Eight |
| c. Base Five | d. Mayan |
Convert 13,595 to Base Twelve
Convert 120,258 to Mayan
Count from 620 to 630 in Base Five
State the numeral that comes just before:
| a. [latex]173 425 760_{\text{eleven}}[/latex] | b. [latex]2 010 212 000_{\text{four}}[/latex] |
State the numeral that comes right after:
| a. [latex]539100TE_{\text{twelve}}[/latex] | b. [latex]3 102 313 444_{\text{five}}[/latex] |
Answer true or false. If false, explain why
| a. [latex]2_{\text{four}} = 2[/latex] | b. [latex]3_{\text{four}} = 3_{\text{twelve}}[/latex] | c. [latex]10_{\text{twelve}} = 10_{\text{five}}[/latex] |
Using Base Three blocks, you had 7 flats, 10 longs and 5 units. What number does this represent in
| a. Base Three? | b. Base Ten? |
Write each number shown in expanded notation as a numeral in the base specified.
| a. [latex]3 \times 7^{8} + 6 \times 7^{5} + 4 \times 7^{4}[/latex] to Base Seven |
| b. [latex]1 \times 3^{10} + 2 \times 3^{9} + 2 \times 3^{3}[/latex] to Base Three |
Write each number in expanded notation:
| a. [latex]200 050 030 000_{\text{nine}}[/latex] |
| b. [latex]1 000 100 001 000_{\text{two}}[/latex] |
Write each numeral in expanded form. Then, convert each numeral to a Base Ten mixed numeral with the fraction simplified.
| a. [latex]43.3_{\text{nine}}[/latex] | b. [latex]35.12_{\text{six}}[/latex] |
| c. [latex]121.21_{\text{three}}[/latex] | d. [latex]333.333_{\text{five}}[/latex] |
Rewrite from expanded form to a numeral in the appropriate base.
| a. [latex]3 \times 4^{2} + 2 \times 4^{0} + 3 \times 4^{-1} + 1 \times 4^{-3}[/latex] |
| b. [latex]5 \times 11^{3} + 10 \times 11^{1} + 8 \times 11^{-1} + 1 \times 11^{-2}[/latex] |
| c. [latex]1 \times 2^{2} + 1 \times 2^{0} + 1 \times 2^{-1} + 1 \times 2^{-4}[/latex] |